Parallel And Perpendicular Lines Worksheet Page 18

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Study Tip
Slopes of Parallel and Perpendicular Lines
Postulates
Postulates
Look Back
3.2
Two nonvertical lines have the same slope if and only if they are parallel.
To review if and only if
3.3
Two nonvertical lines are perpendicular if and only if the product of their
statements, see Reading
Mathematics, page 81.
slopes is
1.
Determine Line Relationships
Example
Example
3
3
Determine whether AB and CD are parallel, perpendicular, or neither.
a. A( 2,
5), B(4, 7), C(0, 2), D(8,
2)
Find the slopes of AB and CD.
TEACHING TIP
7
(
5
)
2
2
slope of AB
slope of CD
4
(
2
)
8
0
1
2
4
1
or 2
or
6
8
2
1
The product of the slopes is 2
or
1. So, AB is perpendicular to CD.
2
b. A( 8,
7), B(4,
4), C( 2,
5), D(1, 7)
4
(
7
)
7
(
5
)
slope of AB
slope of CD
4
(
8
)
1
(
2
)
3
1
1
2
or
or 4
1
2
4
3
The slopes are not the same, so AB and CD are not parallel. The product of the
1
slopes is 4
or 1. So, AB and CD are neither parallel nor perpendicular.
4
The relationships of the slopes of lines can be used to graph a line parallel or
perpendicular to a given line.
Use Slope to Graph a Line
Example
Example
4
4
Graph the line that contains P( 2, 1) and is perpendicular to JK with J( 5,
4)
and K(0,
2).
First, find the slope of JK.
y
y
y
2
1
m
Slope formula
x
x
( 2, 1 )
P
2
1
x
2
(
4
)
O
Substitution
0
(
5
)
rise:
5 units
( 0,
2 )
K
2
Simplify.
5
Q
( 0,
4 )
( 5,
4 )
J
Study Tip
run: 2 units
The product of the slopes of two perpendicular
lines is
1.
Negative Slopes
2
5
To help determine
Since
1, the slope of the line perpendicular
5
2
direction with negative
5
slopes, remember that
to JK through P( 2, 1) is
.
2
5
5
5
.
2
2
2
Graph the line. Start at ( 2, 1). Move down 5 units and then move right 2 units.
Label the point Q. Draw PQ.
Lesson 3-3 Slopes of Lines 141

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